scholarly journals A hybrid preconditioner of banded matrix approximation and alternating direction implicit iteration for symmetric Sinc–Galerkin linear systems

2003 ◽  
Vol 366 ◽  
pp. 317-335 ◽  
Author(s):  
Michael K. Ng ◽  
Zhong-Zhi Bai
Keyword(s):  
Linear Systems ◽  
Matrix Approximation ◽  
Alternating Direction Implicit ◽  
Banded Matrix ◽  
Alternating Direction ◽  
Implicit Iteration

scholarly journals Low-Rank Alternating Direction Implicit Iteration in pyMOR

2020 ◽  
Vol 2 (1) ◽  
pp. 1-13
Author(s):  
Linus Balicki
Keyword(s):  
Large Scale ◽  
Low Rank ◽  
Balanced Truncation ◽  
Lyapunov Equations ◽  
Software Library ◽  
Alternating Direction Implicit ◽  
Truncation Method ◽  
Alternating Direction ◽  
Adi Iteration ◽  
Implicit Iteration

The low-rank alternating direction implicit (LR-ADI) iteration is an effective method for solving large-scale Lyapunov equations. In the software library pyMOR, solutions to Lyapunov equations play an important role when reducing a model using the balanced truncation method. In this article we introduce the LR-ADI iteration as well as pyMOR, while focusing on its features which are relevant for integrating the iteration into the library. We compare the run time of the iteration's pure pyMOR implementation with those achieved by external libraries available within the pyMOR framework.

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